Compound Interest Formula Explained
The math behind compound interest is simpler than it looks. Here's the full formula, broken down step by step, with real worked examples for both lump sums and monthly contributions.
Skip the math — try it yourself
Plug in your numbers and our compound interest calculator runs both formulas instantly. No signup, no spreadsheets — just clear results and a growth chart.
Open Compound Interest CalculatorThe basic compound interest formula
FV = P × (1 + r/n)n×t
- FV = Future value
- P = Principal (initial investment)
- r = Annual interest rate (decimal, so 7% = 0.07)
- n = Number of compounding periods per year (12 for monthly, 1 for annual)
- t = Number of years
Worked example
Invest $10,000 at 7% compounded monthly for 20 years:
- Convert the rate: 7% → 0.07
- Divide by compounding periods: 0.07 / 12 ≈ 0.005833
- Add 1: 1.005833
- Raise to the power of n × t = 12 × 20 = 240: (1.005833)240 ≈ 4.0387
- Multiply by principal: 10,000 × 4.0387 ≈ $40,387
With monthly contributions (annuity formula)
When you also contribute regularly, you need a second formula — the future value of an annuity:
FV = PMT × [((1 + r/n)n×t − 1) / (r/n)]
- PMT = Periodic contribution (e.g. $500/month)
Worked example
Contribute $500/month at 7% compounded monthly for 20 years:
FV = 500 × [((1.005833)240 − 1) / 0.005833] ≈ $260,463
Combining both formulas
When you start with a lump sum and contribute monthly, simply add the two formulas together. Starting with $10,000 plus $500/month at 7% for 20 years gives approximately $300,850 — that's the power of combining a head start with consistent contributions.
The Rule of 72 — a quick shortcut
Need a fast estimate? Divide 72 by your interest rate to find how many years it takes to double your money:
- At 6%: 72 / 6 = 12 years
- At 8%: 72 / 8 = 9 years
- At 12%: 72 / 12 = 6 years
For a deeper conceptual walkthrough, see how compound interest works or compare with simple vs compound interest.
Skip the math — try it yourself
Plug in your numbers and our compound interest calculator runs both formulas instantly. No signup, no spreadsheets — just clear results and a growth chart.
Open Compound Interest CalculatorFrequently Asked Questions
What is the compound interest formula?
The standard compound interest formula is FV = P × (1 + r/n)^(n×t), where FV is the future value, P is the principal (starting amount), r is the annual interest rate as a decimal, n is the number of times interest compounds per year, and t is the number of years.
How do I calculate compound interest with monthly contributions?
When you contribute every month, you add a second formula — the future value of an annuity: FV = PMT × [((1 + r/n)^(n×t) − 1) / (r/n)]. Add this result to the lump-sum future value to get your total. Our compound interest calculator combines both formulas automatically.
What is the difference between APR and APY?
APR (annual percentage rate) is the nominal yearly rate without compounding. APY (annual percentage yield) includes the effect of compounding. At a 6% APR compounded monthly, the APY is about 6.17%. APY is the truer measure of what you'll actually earn.
What is the Rule of 72?
The Rule of 72 is a quick mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes for your money to double. At 8%, money doubles in roughly 9 years (72 / 8). It's accurate enough for rough planning between 4% and 15%.
Can I use the formula for daily compounding?
Yes — set n = 365. So $10,000 at 5% compounded daily for 10 years becomes 10,000 × (1 + 0.05/365)^(365×10) ≈ $16,486. The math is the same; only the compounding frequency changes.
Is the formula the same for loans and mortgages?
The same compounding logic applies, but loans use an amortization formula to solve for the monthly payment that pays off the loan over a fixed term. Try our loan calculator or mortgage calculator to see this in action.